Interpretive Summary: Over the past 50 years, the USDA Natural Resources Conservation Service has aided in the design and/or construction of over 11,000 small watershed dams. As these dams near the end of their design life, problems such as inadequate spillway capacity arise. Roller compacted concrete (RCC) stepped spillways have proven to be a viable rehabilitation solution for increasing spillway capacity of these structures. Many of these spillways are designed wider at the top of the dam than at the bottom in-order to conform to the downstream valley. Converging spillways of this nature require special consideration in design. A comparison of model studies of alternative spillway sidewall designs are reported in this paper. The sidewall designs studied include vertical sidewalls, stepped sloping sidewalls, and smooth sloping sidewalls. Vertical sidewalls and smooth sloping sidewalls result in lower flow run-up elevations for converging sidewalls in comparison to the stepped sloping sidewalls. The results provide necessary information for the engineer to properly dimension the sidewalls to contain the flow within the spillway.

Technical Abstract:
Over the past 50 years, the USDA Natural Resources Conservation Service (NRCS) has aided in the design and/or construction of over 11,000 small watershed dams. As these dams near the end of their 50 year design life problems are arising. A problem for many small earthen dams is inadequate spillway capacity. Roller compacted concrete (RCC) stepped spillways have proven to be a viable rehabilitation solution for increasing spillway capacity of these structures. In some cases the RCC stepped spillway is placed in a section of the earthen embankment, with converging chute training walls conforming to the downstream valley. Converging spillways require special consideration in design because the convergence of the spillway causes a shock wave to occur in the flow along the training walls resulting in increased training wall dimension requirements. Model studies have reported on required dimensions for vertical training walls for RCC Stepped Spillways but little information exists for sloped converging chute training walls. Recent studies on converging stepped spillways with sloped training walls have been conducted to provide this needed information. The studies were conducted at the USDA-Agricultural Research Service (ARS) Hydraulic Engineering Research Unit (HERU) in Stillwater, Oklahoma. The studies utilized a three-dimensional small scale physical model with a representative spillway having a slope of 3(H):1(V) and converging vertical training walls and training walls with slopes of 1:1, 2:1, and 3:1. Both smooth and stepped sloped training walls were tested. Flow information and water surface profiles were collected and examined for each of the modeled configurations. Shock-wave run-up due to convergence at the training walls was observed to be the controlling factor for determining wall dimensions of the vertical wall and smooth training walls but the run-up for the stepped training walls was also impacted by the steps themselves resulting in dramatically different results. Vertical, and stepped and smooth sloped training wall results from these studies are reported and compared in this paper. This research is expected to help in the development of design guidelines for similarly designed structures.